German Patent Application No. 196 45 769 describes a method for allocating a authentication device to a base station. An authentication device designed as a remote control is allocated to a base station belonging to a motor vehicle in particular in a two-step method, the base station emitting a search signal in a first allocation step to detect any authentication devices present within the signal range. Any authentication devices present will receive the search signal, compare it with a reference signal stored in a memory and respond by sending back a "present" signal if the search signal and reference signal match. This sending back takes place at a time which is characteristic of the respective authentication device sending it back and is based on receipt of the call signal. The base station can unambiguously identify which authentication elements are present on the basis of this characteristic time. It then selects one of those present and performs an allocation verification in the second allocation step. This method makes it possible to allocate multiple authentication devices to one base station, and to guarantee that the allocation will be performed rapidly.